Recently, Rippon and Stallard [1]}, [2]} introduced the concept of an
(infinite) spider's web.
This is a connected set \(E\subset {\mathbb {C}}\)  with the
property that there exists a sequence of increasing simply-connected domains
\((G_n)\)  whose union is all of \({\mathbb {C}}\)  such that
\(\partial G_n\subset E\)  for all \(n\) .
Functions whose (fast) escaping set is a spider's web
have some strong dynamical properties.
For instance, every such function has only bounded Fatou components
and there exists no curve to \(\infty \)  on which \(f\)  is bounded
(compare [1]}).
In particular, the set of singular values of \(f\) 
must be unbounded. (For precise definitions see
Section ).
